1. Field of the Invention
The present invention is directed to a method and to an arrangement for modelling a system with non-linear stochastic behavior, particularly a biological system such as, for example, the insulin-glucose metabolism, for which, as well as for other systems, only a small amount of training data is available for training the neural network.
2. Description of the Prior Art
Since measurements of influencing variables for the determination of the state of a technical or physiological system are very involved and complicated to implement, they are often only undertaken at irregular time intervals. For example, a diabetic person only determines his or her blood sugar content 4-5 times a day. If one attempts to produce models of such systems, an added complication is that these behave highly non-linearly and stochastically, so that computerized neural networks seem suitable for their modelling. Such computerized networks are usually utilized in "free-running" mode or in the "teacher-forcing mode" in which current measurements of the time series that is made available to the network replace iterated values. Both approaches are problematical in systems that behave highly stochastically and wherein only a few measured values in the time series are available for the individual influencing variables. It is known from "Lewis, F. L. (1986) Optimal Estimation, John Wiley, N.Y." to approach such problems wih the assistance of stochastic models in which, for example, non-linear condition-space models are employed. However, there is still the problem of predicting and training lacking measured values whose analytical solution leads to such complicated integrals that they are unmanageable. Alternatively thereto, condition-dependent linearizations can be implemented for the prediction and the training, the most popular thereof being the "Extended Kalman Filter". Other possible solutions for such problems are not known in the prior art.